ED_LRR/docs_mdbook/src/intro/fsd_fuel.md

Notes on FSD Fuel consumption and jump range

FSD Fuel consumption (Elite: Dangerous Wiki):

Fuel = 0.001 \cdot l \cdot \left(\frac{dist \cdot \left(m_{fuel} + m_{ship}\right)}{boost \cdot m_{opt}}\right)^{p}

Solving for \(dist\) gives the jump range (in Ly) for a given amount of fuel (in tons) as:

dist = \frac{boost \cdot m_{opt} \cdot \left(\frac{1000.0 \cdot \min\left(f_{max}, m_{fuel}\right)}{l}\right)^{\frac{1}{p}}}{m_{fuel} + m_{ship}}

Assuming \(f_{max}\) tons of available fuel gives us the maximum jump range for a single jump as:

dist_{max} = \frac{boost \cdot m_{opt} \cdot \left(\frac{1000.0 \cdot f_{max}}{l}\right)^{\frac{1}{p}}}{f_{max} + m_{ship}}

Since the guardian FSD booster increases the maximum jump range by \(B_g\) light years we can calculate a correction factor for the fuel consumption as:

 e_{fuel} = 0.001 \cdot l \cdot \left(\frac{boost^{2} \cdot m_{opt} \cdot \left(\frac{1000.0 \cdot \min\left(f_{max}, m_{fuel}\right)}{l}\right)^{\frac{1}{p}}}{B_{g} \cdot \left(m_{fuel} + m_{ship}\right) + boost^{2} \cdot m_{opt} \cdot \left(\frac{1000.0 \cdot \min\left(f_{max}, m_{fuel}\right)}{l}\right)^{\frac{1}{p}}}\right)^{p}

Incorporating \(e_{fuel}\) into the distance equation yields

dist = \frac{boost \cdot m_{opt} \cdot \left(\frac{1000.0 \cdot e_{fuel} \cdot \min\left(f_{max}, m_{fuel}\right)}{l}\right)^{\frac{1}{p}}}{m_{fuel} + m_{ship}}

Expanding \(e_{fuel}\) yields

dist = \frac{boost \cdot m_{opt} \cdot \left(1.0 \cdot \left(\frac{boost^{2} \cdot m_{opt} \cdot \left(\frac{1000.0 \cdot \min\left(f_{max}, m_{fuel}\right)}{l}\right)^{\frac{1}{p}}}{B_{g} \cdot \left(m_{fuel} + m_{ship}\right) + boost^{2} \cdot m_{opt} \cdot \left(\frac{1000.0 \cdot \min\left(f_{max}, m_{fuel}\right)}{l}\right)^{\frac{1}{p}}}\right)^{p} \cdot \min\left(f_{max}, m_{fuel}\right)\right)^{\frac{1}{p}}}{m_{fuel} + m_{ship}}

Finally, Expanding \(dist_{max}\) yields the full equation as

dist = \frac{boost \cdot m_{opt} \cdot \left(\frac{1000000.0 \cdot \left(\frac{boost^{2} \cdot m_{opt} \cdot \left(\frac{1000.0 \cdot \min\left(f_{max}, m_{fuel}\right)}{l}\right)^{\frac{1}{p}}}{B_{g} \cdot \left(m_{fuel} + m_{ship}\right) + boost^{2} \cdot m_{opt} \cdot \left(\frac{1000.0 \cdot \min\left(f_{max}, m_{fuel}\right)}{l}\right)^{\frac{1}{p}}}\right)^{- p} \cdot \min\left(f_{max}, m_{fuel}\right)}{l^{2}}\right)^{\frac{1}{p}}}{m_{fuel} + m_{ship}}

Where:

• \(Fuel\) is the fuel needed to jump (in tons)
• \(l\) is the linear constant of your FSD (depends on the rating)
• \(p\) is the power constant of your FSD (depends on the class)
• \(m_{ship}\) is the mass of your ship (including cargo)
• \(m_{fuel}\) is the amount of fuel in tons currently stored in your tanks
• \(m_{opt}\) is the optimized mass of your FSD (in tons)
• \(f_{max}\) is the maximum amount of fuel your FSD can use per jump
• \(boost\) is the "boost factor" of your FSD (1.0 when jumping normally, 1.5 when supercharged by a white dwarf, 4.0 for a neutron star, etc)
• \(dist\) is the distance you can jump with a given fuel amount
• \(dist_{max}\) is the maximum distance you can jump (when \(m_{fuel}=f_{max}\))
• \(B_{g}\) is the amount of Ly added by your Guardian FSD Booster
• \(e_{fuel}\) is the efficiency increase added by the Guardian FSD Booster